The power of trees
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866915946646470656 |
|---|---|
| author | Brodsky, Ari Meir Rinot, Assaf Yadai, Shira |
| author_facet | Brodsky, Ari Meir Rinot, Assaf Yadai, Shira |
| contents | We give two consistent constructions of trees $T$ whose finite power $T^{n+1}$ is sharply different from $T^n$:
1. An $\aleph_1$-tree $T$ whose interval topology $X_T$ is perfectly normal, but $(X_T)^2$ is not even countably metacompact.
2. For an inaccessible $κ$ and a positive integer $n$, a $κ$-tree such that all of its $n$-derived trees are Souslin and all of its $(n+1)$-derived trees are special. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_26419 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The power of trees Brodsky, Ari Meir Rinot, Assaf Yadai, Shira Logic General Topology Primary 03E35, 54B10. Secondary 54F05, 54D20, 54D15 We give two consistent constructions of trees $T$ whose finite power $T^{n+1}$ is sharply different from $T^n$: 1. An $\aleph_1$-tree $T$ whose interval topology $X_T$ is perfectly normal, but $(X_T)^2$ is not even countably metacompact. 2. For an inaccessible $κ$ and a positive integer $n$, a $κ$-tree such that all of its $n$-derived trees are Souslin and all of its $(n+1)$-derived trees are special. |
| title | The power of trees |
| topic | Logic General Topology Primary 03E35, 54B10. Secondary 54F05, 54D20, 54D15 |
| url | https://arxiv.org/abs/2510.26419 |